# How do you solve 2 log x = log 25 + 2?

Dec 29, 2015

Use the fact that $\log \left(x\right)$ is a one-one function as a Real-valued function of Real numbers to find:

$x = 50$

#### Explanation:

Divide both sides by $2$ to get:

$\log \left(x\right)$

$= \frac{\log \left(25\right) + 2}{2}$

$= \frac{2 \log \left(5\right) + 2 \log \left(10\right)}{2}$

$= \log \left(5\right) + \log \left(10\right)$

$= \log \left(50\right)$

Hence $x = 50$, since $\log \left(x\right) : \left(0 , \infty\right) \to \mathbb{R}$ is one-one.